The adjoint representation inside the exterior algebra of a simple Lie algebra [PDF]
Advances in Mathematics, 2015 Final version. More misprints corrected.
DE CONCINI, Corrado +2 more
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Characterizing barren plateaus in quantum ansätze with the adjoint representation. [PDF]
Nat Commun, 2023 Variational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups.
Fontana E +7 more
europepmc +3 more sources
Multiplicity of the Adjoint Representation in Simple Quotients of the Enveloping Algebra of a Simple Lie Algebra [PDF]
Transactions of the American Mathematical Society, 1989 Let g \mathfrak {g} be a complex simple Lie algebra, h \mathfrak {h} a Cartan subalgebra and U ( g ) U(\mathfrak {g}) the enveloping algebra of g \mathfrak {g} . We calculate for each maximal two-sided
A. Joseph
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The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a ...
Oksana Ye. Hentosh
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The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula
, 2013 Even though weight multiplicity formulas, such as Kostant's formula, exist their computational use is extremely cumbersome. In fact, even in cases when the multiplicity is well understood, the number of terms considered in Kostant's formula is factorial in the rank of the Lie algebra and the value of the partition function is unknown.
Harris, Pamela E. +2 more
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On special covariants in the exterior algebra of a simple Lie algebra [PDF]
, 2014 We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the n-th symmetric power of the ...
De Concini, Corrado +3 more
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On the geometry underlying a real Lie algebra representation [PDF]
, 2012 Let $G$ be a real Lie group with Lie algebra $\mathfrak g$. Given a unitary representation $\pi$ of $G$, one obtains by differentiation a representation $d\pi$ of $\mathfrak g$ by unbounded, skew-adjoint operators.
Le-Bert, Rodrigo Vargas
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Useful relations among the generators in the defining and adjoint representations of SU(N)
SciPost Physics Lecture Notes, 2021 There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc.
Howard E. Haber
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Euler’s difference table and the decomposition of tensor powers of the adjoint representation of the $$A_n$$ Lie algebra [PDF]
Theoretical and mathematical physics, 2019 By using of Euler's difference table, we obtain simple explicit formula for the decomposition of $k$-th tensor power of adjoint representation of $A_n$ Lie algebra at $2 k \le{n+1}$.
A. Perelomov
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Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation [PDF]
Journal of Mathematics and Physics, 2018 In this paper, first we study infinitesimal deformations of a Lie algebra with a representation and introduce the notion of a Nijenhuis pair, which gives a trivial deformation of a Lie algebra with a representation.
Y. Hu, Jiefeng Liu, Y. Sheng
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